Introduction to Bayesian Statistics

Data-driven computational neuroscience facilitates the transformation of data into insights into the structure and functions of the brain. This introduction for researchers and graduate students is the first in-depth, comprehensive treatment of statistical and machine learning methods for neuroscience. The methods are demonstrated through case studies of real problems to empower readers to build their own solutions. The book covers a wide variety of methods, including supervised classification with non-probabilistic models (nearest-neighbors, classification trees, rule induction, artificial neural networks and support vector machines) and probabilistic models (discriminant analysis, logistic regression and Bayesian network classifiers), meta-classifiers, multi-dimensional classifiers and feature subset selection methods. Other parts of the book are devoted to association discovery with probabilistic graphical models (Bayesian networks and Markov networks) and spatial statistics with po

Like the De Groot winning first edition, the second edition of Principles of Uncertainty is an accessible, comprehensive guide to the theory of Bayesian Statistics written in an appealing, inviting st

Decision-making in the face of uncertainty is a significant challenge in machine learning, and the multi-armed bandit model is a commonly used framework to address it. This comprehensive and rigorous introduction to the multi-armed bandit problem examines all the major settings, including stochastic, adversarial, and Bayesian frameworks. A focus on both mathematical intuition and carefully worked proofs makes this an excellent reference for established researchers and a helpful resource for graduate students in computer science, engineering, statistics, applied mathematics and economics. Linear bandits receive special attention as one of the most useful models in applications, while other chapters are dedicated to combinatorial bandits, ranking, non-stationary problems, Thompson sampling and pure exploration. The book ends with a peek into the world beyond bandits with an introduction to partial monitoring and learning in Markov decision processes.

Statistical Concepts-A Second Course presents the last 10 chapters from An Introduction to Statistical Concepts, Fourth Edition. Designed for second and upper-level statistics courses, this book highl

This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introdu

Statistical Concepts-A First Course presents the first 10 chapters from An Introduction to Statistical Concepts, Fourth Edition. Designed for first and lower-level statistics courses, this book commun

A First Course in Probability offers an elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. Through clear and intuitive explana

Primary Mathematics: Integrating Theory with Practice provides a comprehensive introduction to teaching and learning mathematics in today's classrooms. Closely aligned with the Australian Curriculum: Mathematics, this text covers the core learning areas of measurement, space and geometry, early number concepts, data and statistics, chance and probability, and patterns and algebra. The text also addresses key considerations for teachers, such as planning, assessment, differentiation and teaching outside traditional contexts. The third edition has been thoroughly revised and features three new chapters focusing on the General Capabilities and Cross-Curricular Priorities, implementing STEM strategies in the primary setting, and the transition to practice. Each chapter highlights how the theory of teaching mathematics can be put into practice effectively and includes new guided reflective questions and student tasks. Written by an expert author team, Primary Mathematics remains an essentia

For one- or two-semester courses in Probability, Probability & Statistics, or Mathematical Statistics. An authoritative introduction to an in-demand field Advances in computing technology &n

This Handbook provides a compendium of research methods that are essential for studying interaction and communication across the behavioral sciences. Focusing on coding of verbal and nonverbal behavior and interaction, the Handbook is organized into five parts. Part I provides an introduction and historic overview of the field. Part II presents areas in which interaction analysis is used, such as relationship research, group research, and nonverbal research. Part III focuses on development, validation, and concrete application of interaction coding schemes. Part IV presents relevant data analysis methods and statistics. Part V contains systematic descriptions of established and novel coding schemes, which allows quick comparison across instruments. Researchers can apply this methodology to their own interaction data and learn how to evaluate and select coding schemes and conduct interaction analysis. This is an essential reference for all who study communication in teams and groups.

This Handbook provides a compendium of research methods that are essential for studying interaction and communication across the behavioral sciences. Focusing on coding of verbal and nonverbal behavior and interaction, the Handbook is organized into five parts. Part I provides an introduction and historic overview of the field. Part II presents areas in which interaction analysis is used, such as relationship research, group research, and nonverbal research. Part III focuses on development, validation, and concrete application of interaction coding schemes. Part IV presents relevant data analysis methods and statistics. Part V contains systematic descriptions of established and novel coding schemes, which allows quick comparison across instruments. Researchers can apply this methodology to their own interaction data and learn how to evaluate and select coding schemes and conduct interaction analysis. This is an essential reference for all who study communication in teams and groups.

This richly illustrated book provides an easy-to-read introduction to the challenges of organizing and integrating modern data worlds, explaining the contribution of public statistics and the ISO stan

Actuaries have access to a wealth of individual data in pension and insurance portfolios, but rarely use its full potential. This book will pave the way, from methods using aggregate counts to modern developments in survival analysis. Based on the fundamental concept of the hazard rate, Part I shows how and why to build statistical models, based on data at the level of the individual persons in a pension scheme or life insurance portfolio. Extensive use is made of the R statistics package. Smooth models, including regression and spline models in one and two dimensions, are covered in depth in Part II. Finally, Part III uses multiple-state models to extend survival models beyond the simple life/death setting, and includes a brief introduction to the modern counting process approach. Practising actuaries will find this book indispensable, and students will find it helpful when preparing for their professional examinations.

For courses in Multivariate Statistics, Marketing Research, Intermediate Business Statistics, Statistics in Education, and graduate-level courses in Experimental Design and Statistics. Appropriate for experimental scientists in a variety of disciplines, this market-leading text offers a readable introduction to the statistical analysis of multivariate observations. Its primary goal is to impart the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. Ideal for a junior/senior or graduate level course that explores the statistical methods for describing and analyzing multivariate data, the text assumes two or more statistics courses as a prerequisite.

This textbook provides a clear, concise, and comprehensive introduction to methodological issues encountered by the various social science disciplines. It emphasizes applications, with detailed examples, so that readers can put these methods to work in their research. Within a unified framework, John Gerring and Dino Christenson integrate a variety of methods - descriptive and causal, observational and experimental, qualitative and quantitative. The text covers a wide range of topics including research design, data-gathering techniques, statistics, theoretical frameworks, and social science writing. It is designed both for those attempting to make sense of social science, as well as those aiming to conduct original research. The text is accompanied by online practice questions, exercises, examples, and additional resources, including related readings and websites. An essential resource for undergraduate and postgraduate programs in communications, criminal justice, economics, business,

A comprehensive guide to data analysis techniques for physical scientists, providing a valuable resource for advanced undergraduate and graduate students, as well as seasoned researchers. The book begins with an extensive discussion of the foundational concepts and methods of probability and statistics under both the frequentist and Bayesian interpretations of probability. It next presents basic concepts and techniques used for measurements of particle production cross-sections, correlation functions, and particle identification. Much attention is devoted to notions of statistical and systematic errors, beginning with intuitive discussions and progressively introducing the more formal concepts of confidence intervals, credible range, and hypothesis testing. The book also includes an in-depth discussion of the methods used to unfold or correct data for instrumental effects associated with measurement and process noise as well as particle and event losses, before ending with a presentati

This book provides an advanced introduction to the science behind automated prediction systems, focusing on sea ice analysis and forecasting. Starting from basic principles, fundamental concepts in sea ice physics, remote sensing, numerical methods, and statistics are explained at an accessible level. Existing operational automated prediction systems are described and their impacts on information providers and end clients are discussed. The book also provides insight into the likely future development of sea ice services and how they will evolve from mainly manual processes to increasing automation, with a consequent increase in the diversity and information content of new ice products. With contributions from world-leading experts in the fields of sea ice remote sensing, data assimilation, numerical modelling, and verification and operational prediction, this comprehensive reference is ideal for students, sea ice analysts, and researchers, as well as decision-makers and professionals

This textbook provides a clear, concise, and comprehensive introduction to methodological issues encountered by the various social science disciplines. It emphasizes applications, with detailed examples, so that readers can put these methods to work in their research. Within a unified framework, John Gerring and Dino Christenson integrate a variety of methods - descriptive and causal, observational and experimental, qualitative and quantitative. The text covers a wide range of topics including research design, data-gathering techniques, statistics, theoretical frameworks, and social science writing. It is designed both for those attempting to make sense of social science, as well as those aiming to conduct original research. The text is accompanied by online practice questions, exercises, examples, and additional resources, including related readings and websites. An essential resource for undergraduate and postgraduate programs in communications, criminal justice, economics, business,

Targeted at graduate students, researchers and practitioners in the field of science and engineering, this book gives a self-contained introduction to a measure-theoretic framework in laying out the definitions and basic concepts of random variables and stochastic diffusion processes. It then continues to weave into a framework of several practical tools and applications involving stochastic dynamical systems. These include tools for the numerical integration of such dynamical systems, nonlinear stochastic filtering and generalized Bayesian update theories for solving inverse problems and a new stochastic search technique for treating a broad class of non-convex optimization problems. MATLAB® codes for all the applications are uploaded on the companion website.

Introduction to Real World Statistics provides students with the basic concepts and practices of applied statistics, including data management and preparation; an introduction to the concept of probab

Introduction to Real World Statistics provides students with the basic concepts and practices of applied statistics, including data management and preparation; an introduction to the concept of probab

Scheck’s textbook starts with a concise introduction to classical thermodynamics, including geometrical aspects. Then a short introduction to probabilities and statistics lays the basis for the statis

Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.

Accessible and concise, with minimal mathematics, this fourth edition of a classic textbook on multivariate statistics is perfect as an introduction to the subject for non-statisticians. It covers all

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction

This book is designed as a practical and intuitive introduction to probability, statistics and random quantities for physicists. The book aims at getting to the main points by a clear, hands-on exposi

This book begins with an introduction to PBXs (Private Branch Exchanges) and the scene, statistics and involved actors. It discusses confidentiality, integrity and availability threats in PBXs. The au

Gathering the right kind and the right amount of information is crucial for any decision-making process. This book presents a unified framework for assessing the value of potential data gathering schemes by integrating spatial modelling and decision analysis, with a focus on the Earth sciences. The authors discuss the value of imperfect versus perfect information, and the value of total versus partial information, where only subsets of the data are acquired. Concepts are illustrated using a suite of quantitative tools from decision analysis, such as decision trees and influence diagrams, as well as models for continuous and discrete dependent spatial variables, including Bayesian networks, Markov random fields, Gaussian processes, and multiple-point geostatistics. Unique in scope, this book is of interest to students, researchers and industry professionals in the Earth and environmental sciences, who use applied statistics and decision analysis techniques, and particularly to those wor

Offering a clear introduction to the basics of psychological testing as well as to psychometrics and statistics,Foundations of Psychological Testing: A Practical Approach, Fifth Editionby Leslie A. Mi

Provides an understanding of statistics in the social sciences. This best-selling introduction to statistical analysis in the social sciences provides the right balance of conceptual understandin

With its engaging and conversational tone, Essential Biostatistics: A Nonmathematical Approach provides a clear introduction to statistics for students in a wide range of fields, and a concise statist

This celebrated primer presents an introduction to all of the key ingredients in understanding computerized adaptive testing technology, test development, statistics, and mental test theory. Based on

This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Fréchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicia

Do you have a biological question that could be readily answered by computational techniques, but little experience in programming? Do you want to learn more about the core techniques used in computational biology and bioinformatics? Written in an accessible style, this guide provides a foundation for both newcomers to computer programming and those interested in learning more about computational biology. The chapters guide the reader through: a complete beginners' course to programming in Python, with an introduction to computing jargon; descriptions of core bioinformatics methods with working Python examples; scientific computing techniques, including image analysis, statistics and machine learning. This book also functions as a language reference written in straightforward English, covering the most common Python language elements and a glossary of computing and biological terms. This title will teach undergraduates, postgraduates and professionals working in the life sciences how t

The book opens with a short introduction to Indian music, in particular classical Hindustani music, followed by a chapter on the role of statistics in computational musicology. The authors then show h

If you know how to program, you have the skills to turn data into knowledge using the tools of probability and statistics. This concise introduction shows you how to perform statistical analysis compu

This book contains hands-on exercises for a full semester course in statistics for undergraduate geographers. The workbook follows the chapters in An Introduction to Statistical Problem Solving for Ge

Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook is an accessible introduction to the field of optimization, focusing on powerful and reliable convex optimization techniques. Students and practitioners will learn how to recognize, simplify, model and solve optimization problems - and apply these principles to their own projects. A clear and self-contained introduction to linear algebra demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance. Requiring only a basic understanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and rigor, it enables students to quickly understand the material, without being overwhelmed by complex mathematics. Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and relevant examples from diverse fields including engineering, data

Based around a series of real-life scenarios, this engaging introduction to statistical reasoning will teach you how to apply powerful statistical, qualitative and probabilistic tools in a technical context. From analysis of electricity bills, baseball statistics, and stock market fluctuations, through to profound questions about physics of fermions and bosons, decaying nuclei, and climate change, each chapter introduces relevant physical, statistical and mathematical principles step-by-step in an engaging narrative style, helping to develop practical proficiency in the use of probability and statistical reasoning. With numerous illustrations making it easy to focus on the most important information, this insightful book is perfect for students and researchers of any discipline interested in the interwoven tapestry of probability, statistics, and physics.